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Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we introduce a new production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is NP-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the effectiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

International audience ; Waste accumulation in landfills, global warming and the need to preserve finite raw materials push governments and industries to shift towards a circular economy. Industrial symbiosis represents a sustainable way of sharing resources and converting unavoidable production residues into useful and added-value products. In this context, we study a production planning problem arisen between two production units (PU) within an industrial symbiosis. During the production process of a main product, a production residue is generated by the first PU, which is subsequently either used as raw materials by the second PU, or disposed of. The second PU can also purchase raw materials from an external supplier. The resulting combined production planning problem has been formulated as a two-level single-item lot-sizing problem. We prove that this problem is N P-Hard irrespective of the production residue, namely unstorable, or storable with a limited capacity. To efficiently solve this problem, a heuristic based on Lagrangian decomposition is proposed. Extensive numerical experiments highlight the competitiveness of the proposed solution method. The impact of the collaborative framework, in which the production plans of each PU are brought together, has been studied via a comparative analysis of different decentralized and centralized collaboration policies. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up an industrial symbiosis between a supplier of by-products and its receiver.

The presented work combines two areas of research: cooperative game theory and lot size optimization. One of the most essential problems in cooperations is to allocate cooperative profits or costs among the partners. The core is a well known method from cooperative game theory that describes efficient and stable profit/cost allocations. A general algorithm based on the idea of constraint generation to compute core elements for cooperative optimization problems is provided. Beside its application for the classical core, an extensive discussion of core variants is presented and how they can be handled with the proposed algorithm. The second part of the thesis contains several cooperative lot sizing problems of different complexity that are analyzed regarding theoretical properties like monotonicity or concavity and solved with the proposed row generation algorithm to compute core elements; i.e. determining stable and fair cost allocations.

The purchasing function is growing in importance in today's industrial economy. In many purchasing situations there are a number of conflicting considerations that influence the final purchasing decision. The professional purchasing person must make profitable buying decisions under these circumstances. The single item purchase lot sizing literature in the past has served as the foundation for developing and studying the requirements planning based models and techniques. The purchasing manager's methods for making quantity (lot size) decisions are examined. Significant literature on the subject is classified and a taxonomy provided. Variations within the purchase lot sizing literature are discussed. Purchase lot sizing literature has important limitations by focusing exclusively on lot sizing as the relevant criterion for making economic order size decisions. A logical extension would be to include, the economic performance of alternative lot size procedures in a capacitated Materials Requirement Planning (MRP) environment. Another extension should consider the economics of jointly ordering from one vendor.

ABSTRACTOften, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price‐break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules.This paper presents a total setup lot‐sizing model that reduces the computations required to find the least‐total‐cost quantity, given parameters from a supplier's price schedule.The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot‐sizing model is next developed to define a "critical interval" that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.

A comprehensive review of the literature for the problem of
lot‐size scheduling (serial and assembly) considering the uncapacitated
problem and complicated capacitated assembly manufacturing structure.
Analyses the different solution techniques and findings for each product
set.

AbstractIn this article, we study deterministic dynamic lot‐sizing problems with a service‐level constraint on the total number of periods in which backlogs can occur over a finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS‐SL‐I) and study the structure of its solution. We show that an optimal solution to this problem can be found in
\documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal O(n^2\kappa)\end{align*} \end{document}
time, where n is the planning horizon and
\documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\kappa=\mathcal O(n)\end{align*} \end{document}
is the maximum number of periods in which demand can be backlogged. Using the proposed shortest path algorithms, we develop alternative tight extended formulations for LS‐SL‐I and one of its relaxations, which we refer to as uncapacitated lot sizing with setups for stocks and backlogs. {We show that this relaxation also appears as a substructure in a lot‐sizing problem which limits the total amount of a period's demand met from a later period, across all periods.} We report computational results that compare the natural and extended formulations on multi‐item service‐level constrained instances. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

AbstractWe consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the "Early Purchase" (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.

AbstractWe consider a dynamic lot‐sizing model with production time windows where each of n demands has earliest and latest production due dates and it must be satisfied during the given time window. For the case of nonspeculative cost structure, an O(nlogn) time procedure is developed and it is shown to run in O(n) when demands come in the order of latest production due dates. When the cost structure is somewhat general fixed plus linear that allows speculative motive, an optimal procedure with O(T4) is proposed where T is the length of a planning horizon. Finally, for the most general concave production cost structure, an optimal procedure with O(T5) is designed. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

AbstractThis paper examines the impact of a rolling‐schedule implementation on the performance of three of the better known lot‐sizing methods for single‐level assembly systems——Part‐Period‐Cost‐Balancing, Silver‐Meal, and Wagner‐Whitin algorithms—and a modified version of the Silver‐Meal procedure. The main finding is that under certain conditions the computationally simpler Silver‐Meal heuristic can provide cost performance superior to that of the Wagner‐Whitin algorithm.